Question

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Question


Given the two right triangles, △
BQP and △
NTP picture above, are the two triangles similar? Why or why not?

(1 point)
Responses

Yes, △
BQP and △
NTP are similar because <Q is equal to <T
Yes, triangleBQP and triangleNTP are similar because

No, △
BQP and △
NTP are not similar because <Q is not equal to < T
No, triangleBQP and triangleNTP are not similar because

No, △
BQP and △
NTP are not similar because <Q is not equal to < TPN
No, triangleBQP and triangleNTP are not similar because

Yes, △
BQP and △
NTP are similar because they both have a right angle
Yes, triangleBQP and triangleNTP are similar because they both have a right angle
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Answer 1

To determine whether the two triangles, △BQP and △NTP, are similar, we can use the criteria for triangle similarity, which include:

1. AA (Angle-Angle) similarity: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
2. SSS (Side-Side-Side) similarity: If the sides of two triangles are in proportion, the triangles are similar.
3. SAS (Side-Angle-Side) similarity: If two sides of one triangle are in proportion to two sides of another triangle, and the included angles are equal, the triangles are similar.

Based on the options provided, if <Q is equal to <T and both triangles have a right angle, then you can establish that:

- Yes, △BQP and △NTP are similar because <Q is equal to <T.

If both triangles have a right angle and at least one angle is equal, that satisfies the AA criterion, confirming they are similar triangles.

Therefore, the correct response would be:

**Yes, △BQP and △NTP are similar because <Q is equal to <T.**